The ability to create three-dimensional (3D) vascularized tissues on demand could enable scientific and technological advances in tissue engineering, drug screening, toxicology, 3D tissue culture, and organ repair. To produce 3D engineered tissue constructs that mimic natural tissues and, ultimately, organs, several key components—cells, extracellular matrix (ECM), and vasculature—may need to be assembled in complex arrangements. Each of these components plays a vital role: cells are the basic unit of all living systems, ECM provides structural support, and vascular networks provide efficient nutrient and waste transport, temperature regulation, delivery of factors, and long-range signaling routes. Without perfusable vasculature within a few hundred microns of each cell, three-dimensional tissues may quickly develop necrotic regions. The inability to embed vascular networks in tissue constructs has hindered progress on 3D tissue engineering for decades.